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Themechanicalbehaviorofnanoscalemetallicmultilayers:Asurvey

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DOI:10.1007/s10409-015-0401-1

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Acta Mech SinDOI 10.1007/s10409-015-0401-1

REVIEW PAPER

The mechanical behavior of nanoscale metallic multilayers:A survey

Q. Zhou1 · J. Y. Xie1 · F. Wang2 · P. Huang1 · K. W. Xu1 · T. J. Lu2

Received: 28 October 2014 / Revised: 27 November 2014 / Accepted: 22 December 2014© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag BerlinHeidelberg 2015

Abstract The mechanical behavior of nanoscale metallicmultilayers (NMMs) has attracted much attention from bothscientific and practical views. Compared with their mono-lithic counterparts, the large number of interfaces existing inthe NMMs dictates the unique behavior of this special classof structural composite materials. While there have been anumber of reviews on the mechanical mechanism of micro-laminates, the rapid development of nanotechnology broughta pressing need for an overview focusing exclusively on aproperty-based definition of theNMMs, especially their size-dependent microstructure andmechanical performance. Thisarticle attempts to provide a comprehensive and up-to-datereview on the microstructure, mechanical property and plas-tic deformation physics ofNMMs.We hope this review couldaccomplish two purposes: (1) introducing the basic conceptsof scaling and dimensional analysis to scientists and engi-neers working on NMM systems, and (2) providing a betterunderstanding of interface behavior and the exceptional qual-ities the interfaces in NMMs display at atomic scale.

Keywords Multilayer · Interface · Microstructure ·Mechanical behavior

B F. Wangwangfei@mail.xjtu.edu.cn

B T. J. Lutjlu@mail.xjtu.edu.cn

1 State-Key Laboratory for Mechanical Behavior of Material,Xi’an Jiaotong University, Xi’an 710049, China

2 State-Key Laboratory for Mechanical Structure Strength andVibration, Xi’an Jiaotong University, Xi’an 710049, China

1 Introduction

Nanoscale metallic multilayer (NMM) films, consistingof two or three thin alternating metallic laminated phaseswith nanoscale dimensions, are a special class of nanoscalecomposite materials. In micromechanical devices, NMMscan play a leading role due to their desirable mechanicalproperties, such as order-of-magnitude increase in strength[1–4], increased ductility and fracture toughness [5–8], resis-tance to radiation damage [9–12], resistance to shock damage[13,14], and thermal stability [15–17], as well as betterelectrical and magnetic responses [18–20]. As materials sci-entists, one of the most basic concepts we learn is that due tothe prevalence of defects, the theoretical strength of a givenmaterial is rarely realized. We have long accepted this asa fact of life when dealing with real materials. However,it has been established that the yield strength of an NMMcomposite can approach one half to one third of the theo-retical strength limit μ/30, μ being the shear modulus ofits constituent metal, reaching GPa level [3]. As a result,an essential concept evolving from the mechanical behaviorof the NMM composite is that unlike bulk composites thatfollow the rule-of-mixtures design philosophy, the volumefraction of its constituent phase is no longer a key para-meter. Rather, it is the density and interfacial structure thatcontrol the strength and fracture of NMM films. In particu-lar, the well-defined, near continuous NMM films provideessential conditions for accurate understanding and char-acterization of relevant interfacial structure and properties.As the idea of interface engineering has existed in variouscommunities for many years, helpful for the design of highperformance multilayer thin films and nanostructured com-posites, the main focus of this article is placed upon recentefforts in this field, covering (interfacial) microstructure,

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mechanical properties, and plastic deformation mechanismsof NMMs.

2 Microstructure

2.1 Synthesis

NMMs with high interfacial content may be fabricatedvia bottom-up, near-equilibrium, thermodynamic techniquessuch as physical vapor deposition (PVD) and electrodeposi-tion (ED) of two different metals that alternate many times,starting with a suitable substrate, until a desired thickness isreached. Different fabrication methods may exert differenteffects on the structure of the resulting multilayer, includ-ing control of scale, crystallographic texture, and residualstresses in the as-fabricated system.

PVD, using such tools as e-beam evaporation or mag-netron sputtering, is the most commonly applied approach tofabricate two-dimensional (2D) planar nanocomposites hav-ing controllable phase sizes down to nanoscale as well ashigh thermal stabilities. It relies on physical mechanismsto produce source atoms in the gaseous state, which arethen deposited onto a substrate in the form of 2D planarcomposites consisting of an alternating stack of two dif-ferent metals. In the case of PVD-deposited multilayers,the interface, across which the metals are immiscible, canbe relatively chemically sharp and ordered, as shown inFig. 1a [5], which is consistent with molecular dynamics(MD) simulations [9,21]. Epitaxy and interface characterare thermodynamically driven, defined by minimization ofthe energy associated with growth processes under a knownset of deposition conditions, such as temperature, substrate,and deposition rate [22]. PVD is more commonly used fortwo main reasons: (1) it is not limited to particular materials;

(2) growth-induced residual stresses and flaws/porosity areminimized.

However, for NMMs fabrication, PVD is relatively slowcompared to other methods and thus the resulting overallmultilayer thickness is limited. Figure 1b shows a mag-netron sputteredAg/Wmultilayerwith an individualAg layerthickness of 20 nm [23],where thewaviness and broken inter-face structure is attributed to an island growth phenomenon.Under non-equilibrium conditions, the growth is dominatedby limitations to themobility of deposited atoms, such as sur-face diffusion, Ehrlich–Schwoebel (ES) effect and depositionrate [24–26]. Two competitive mechanisms—rougheningand smoothing—have been proposed to explain the morpho-logical evolution (e.g., waviness) in NMMs. The wavinessincreases with continued deposition (increasing film thick-ness, Fig. 1c) [27],whichmaybe attributed to the coalescenceof islands during sputtering. For instance, during the sput-tering of very thin layers, individual islands would form,followed by gradual coalescence of such individual islands.Apart from film thickness, numerical simulation results alsoindicated that volume fraction and inhomogeneity as well asanisotropy can play important roles in morphological insta-bilities in NMMs [28]. Surface energy is very sensitive tosurface conditions.Defects created during growth, e.g.,misfitdislocations, have a strong effect on growth. As growth pro-ceeds, however, due to lattice misfit, when the strain energyexceeds a critical value it is energetically favorable to intro-duce misfit dislocations. Subsequently, islands are formedto relieve the misfit strain [28]. As a consequence, layer-by-layer growth followed by island growth is preferred.

Compared to PVD, the method of ED has a lower cost andfaster low-temperature deposition rate. The synthesis of filmsusing ED has a long history, and the overall sample thicknessachieved is sufficient to make self-supported foils with tech-nical ease. In addition, itwas shown in the early 1990s thatED

Fig. 1 a HRTEM image of sharp and ordered interfaces in a Cu–Nb PVD nanolayered composite. b Representative TEM image of Ag20W10,with lines and boxes used to denote the broken modulation structure in the multilayer. c Numerical simulation of morphology evolution. Reprintedfrom Refs. [5,23,27] with permission

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The mechanical behavior of nanoscale metallic multilayers: A survey

was capable of producing multilayered magnetic nanostruc-tures exhibiting a significant giantmagnetoresistance (GMR)effect. Bakonyi and Peter [29] critically evaluated existingGMR results for various element combinations accessible tothe ED technique for the preparation of multilayer films.

In spite of the relative simplicity and cost-effectiveness,ED is rarely used in practice because impurity concentrationhas not been well controlled and the interfaces in ED mul-tilayers are not atomically sharp [30]. Figure 2a shows thecantedmicrostructure of an EDCu–Nimultilayer [31], whileFig. 2b presents the fibermorphology in aNi81Cu19/Cumul-tilayer [32].

2.2 Grain morphology

Acting as a kind of polycrystalline material, the morphologyof grains inside individual NMM layers should be addressedin advance. Because of different restrictions from the inter-faces, three kinds of grain morphologies are common inNMMs, as shown schematically in Fig. 3 [33]. Figure 3a rep-resents multilayers having approximately equal-axed grains,namely, the in-plane lateral grain size is close to individuallayer thickness h, such as Ag/Co [34] and Ag/Cu multi-layers [35]. Figure 3b represents the grain morphology ofcompressed grains whose in-plane grain size is several timeslarger than h, such as Cu/W [36] and Ag/Ni [37]. Figure 3crepresents heterophase layers grown by coherent epitaxyon each other to form a superlattice columnar microstruc-ture, such as Cu/Ni [38,39], Cu/Co [40,41], Cu/Nb [42,43],and Ni/Ru [17]. For an NMM film, surface energy betweenconstituent layers and lattice constant relationship are twokey factors dictating its grain morphologies. When surfaceenergy difference is small, the constituent layers can formclosely packedplane textures parallel to each other.Addition-ally, if the atomic radius ratio rAB satisfies certain conditions,the multilayer film adopts epitaxial growth at the interfaces,forming a superlattice structure; see Fig. 3c–3d. Bauer [44]suggested that a superlattice structure may be characterizedby surface energymismatchΓAB and atomic radiusmatchingrAB, as:

ΓAB = 2 |(γA − γB)/(γA + γB)| ,rAB = aB/aA, (1)

where γ is the surface energy and a is atomic radius. ForΓAB < 0.5 and rAB ≤ 1.00, superlattice formation shouldbe possible; otherwise, NMMs tend to form layered structureparallel to each other. When the in-plane grain size is muchlarger than the single layer thickness h (usually 8–10 timesh), the NMMfilmmay adopt a compressed grain structure inthe form of columnar crystal growth within the single layer,but discontinued at the interfaces (Fig. 3b).

2.3 Thermal stability

The effect of thermal stability on grain/layer morphology hasalso been extensively investigated. In polycrystalline mul-tilayer systems, the free energies of interfaces and grainboundaries will determine the relative stability of each layeras well as the overall stability of the multilayer [46]. Forinstance, in both the annealed Ag/Ni and Cu/Nb multilay-ers shown in Fig. 4 [46], deeper grooves extended intothe layer to induce breakdown and pinch-off. This behav-ior has also been observed in a number of other NMMsystems. However, Misra et al. [15] discovered that poly-crystalline Cu/Nb multilayers with layer thickness greaterthan 35 nm exhibited long-term thermal stability at tempera-tures as high as 80 % of the absolute melting temperatureof Cu. In the annealed films, continuity of the layeredstructure was maintained and the layer thickness remainedunchanged. It was found that zigzag alignment of triple-point junctions (Fig. 5a) and approximate alignment of grainboundaries (Fig. 5b) were both likely to occur in NMMs.The development of zigzag alignment of triple-point junc-tions can effectively impede the development of grooves,contributing, therefore, to morphological stability. Nanolay-ers were observed to be offset by shear at zigzag-alignedtriple-point junctions with equilibrium groove angles [47].Wan et al. [48] found that zigzag microstructures experi-mentally observed in multilayers would form if grains ineach upper layer had a relative shift less than half the in-plane grain size of the lower layer, driven by imbalanceof tensions in interphase and grain boundaries. In termsof the aspect ratio of grain dimensions and the ratio ofthe distance between two nearest triple junctions to the in-plane grain size, Wan et al. [48] also developed stabilitymap of layered structure in Cu/Nb systems using numericalsimulations.

2.4 Atomic interface structure

The atomic interface structure is arguably the most represen-tative internal microstructure of NMMs. Based on continuityof slip planes across an interface, interfaces in NMMs maybe grouped into three categories: coherent interfaces, semi-coherent interfaces, and incoherent interfaces.

Coherent interfaces are commonly found in face-centeredcubic/face-centered cubic (fcc/fcc) NMMs with cube-on-cube structure, such as Cu/Ni, where the two material layersacross the interface have identical crystallographic structureand similar lattice parameters. Slip systems are nearly con-tinuous in coherent interfaces, and there is no discontinuitybetween slip directions of the two layers. Therefore, disloca-tions can pass from one layer to another through coherent (orso-called transparent) interfaces. Nonetheless, a small latticemismatch is usually present at coherent interfaces, leading

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Fig. 2 a Cross-sectional SEM image of Cu–Ni multilayer with individual layer thickness h = 100 nm, showing canted effect. b Plane-view TEMimage of Ni81Cu19 (10 nm)/Cu (1.4 nm) multilayer, showing fiber texture. Reprinted from Refs. [31,32] with permission

Fig. 3 Schematic of three kinds of grain morphologies: a Equal-axed grains. b Compressed grains. c Columnar grains. d Superlattice structureformed in Cu/Ru. Reprinted from Refs. [33,45] with permission

to very strong interfaces with high coherent stresses. Thehigh coherent stresses are barriers the dislocations need toovercome to transmit to the other layers. The role played bycoherent interfaces in the plastic deformation of NMMs willbe discussed in more detail in Sect. 4.1.3.

Similar to coherent interfaces, the two layers of materialsacross a semi-coherent interface have the same crystallo-graphic structure, but there exists a large lattice mismatchalong the relaxed interface, resulting in a relative low shearresistance interface. This type of interface commonly appears

Fig. 4 SEM image of a Ag/Ni and b Cu/Nb multilayer specimens, with evident breakdown of nickel layers (dark layers) in a and pinch-off in Nblayers (light layers) in b. Reprinted from Ref. [46] with permission

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The mechanical behavior of nanoscale metallic multilayers: A survey

Fig. 5 Microstructures of 75 nm Cu/Nb multilayers after 1 h annealing under different temperature: a 1073 K and b 873 K. Note that the zigzagalignment of triple junctions in a and the approximate alignment of grain boundaries (marked by white lines) in b. Reprinted from Ref. [15] withpermission

in face-centered cubic/hexagonal close-packed (fcc/hcp)NMMs. To reduce the high lattice distortion, misfit dislo-cations are often introduced. Therefore, in the absence of amisfit, a semi-coherent interface can easily transform into acoherent one when the layer thickness is smaller than a crit-ical thickness hc for coherency loss. More details about theevolution of interface structure will be presented later.

Incoherent interfaces are interfaces between layers hav-ing distinct lattice structures and high lattice mismatch,with no continuity between slip systems of adjacent layers.This type of interface is commonly found in face-centeredcubic/body-centered cubic (fcc/bcc) NMMs, such as Cu/Nb[49,50]. TEM characterization (Fig. 6a) and atomistic sim-ulations (Fig. 6b) have shown that the Cu/Nb interfacesjoin {111}fcc//{110}bcc planes. The {110}bcc//{111}fcc,〈111〉bcc//〈110〉fcc interface is considered as a “self-healing”interfacial structure that satisfies the Kurdjumov–Sachs(K–S) orientation relationship. Meanwhile, the Nishiyama–Wasserman (N–W) {110}bcc‖{111}fcc, 〈100〉bcc//〈110〉fccorientation relationship has also been reported as a low-energy interface [49], as shown in Fig. 6c. These twointerfaces differ only by a rotation slightly greater than ∼5◦about the interface normal {110}bcc‖{111}fcc.

Incoherent interfaces with wide and mobile misfit dis-locations are less stable than semi-coherent ones. Whensubjected to external loading, an incoherent interface mayshear easily with core spreading because of its low shearstrength relative to that of the layers, as shown in Fig. 7[51]. Wang [52,53] studied the interaction of dislocationswith incoherent interfaces using atomistic simulations andfound that the shear resistance of Cu–Nb interfaces is:(1) lower than the theoretical estimation of shear strengthfor perfect crystals, (2) strongly anisotropic, (3) spatiallynon-uniform, and (4) strongly dependent on the atomicstructure of the interface. Although incoherent systems tendnot to have large coherency stresses as coherent ones,their strengthening mechanism is more complex due to low

interfacial shear strength and the resultant trapping of mobiledislocations [54].

Relative to dislocation trapping, the nucleation of dislo-cations from an interface has received far more attention.For monolithic materials with large grain sizes, the disloca-tion sources within grain interiors are ubiquitous, operatingtypically at low stresses. In contrast, for multilayers withsmall (nanoscale) individual layer thicknesses, the disloca-tion sources are shifted to the interfaces, and the stressesneeded to operate these sources depend on the interfa-cial structure and the interaction with mobile dislocations.Recently, atomic-scale modeling has been used to study dis-location nucleation from Cu/Nb PVD interfaces (either theK–S interface or theN–W interface) [55,56]. The results sug-gested that slight changes in interface structure could havea profound influence on which slip systems are activated inadjoining crystals.

2.5 Interface-facilitated twinning

Nanotwinned (NT) microstructures have recently receivedsignificant attention due to their impressive contributions tomechanical, thermal and electrical performances [57–60].In terms of impeding the transmission of dislocations, twinboundaries (TBs) act in a way similar to high-angle grainboundaries (GBs), allowing NT metals to display extraordi-nary strength. Additionally, TBs are both efficient sinks fordislocations and active sources formobile partial dislocations[61,62]. Hence, TBs play a vital role in the work hardeningcapability, strain rate sensitivity, and ductility of NT met-als [63]. Within the material family of NMMs, high densitystacking faults (SFs) and twins are observed even when h isreduced to 1 nm [39,64]. In the following, the role played byinterface in the formation of twins in NMMs is discussed.

In general, as low stacking fault energy (SFE) is necessaryfor metals to form high density twins, such as 330 stainlesssteel, Ag and Cu, it is challenging to produce such twins

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Fig. 6 a HRTEM image of a KS {111}fcc//{110}bcc interface inCu–Nb NMM. b atomistic modeling of a Cu–Nb bilayer represent-ing KS {111}fcc//{110}bcc interface. c HRTEM image of a NW{111}fcc//{110}bcc interface. Reprinted from Refs. [49,50] with per-mission

in high SFE metals, such as Ni and Al. The formation ofhigh density nanotwins in systems of high SFE is anothermajor challenge. However, fabricating NMMs is an effectivetechnique to introduceNTs into highSFEmetals,which leadsto the high mechanical strength of NMMs. Coherent twin

Fig. 7 Simulation result of core spreading of glide dislocation withininterfaces. Arrows indicate the magnitudes and directions of disregistryvectors. Reprinted from Ref. [51] with permission

interfaces have been clearly found in epitaxial 1 nm Cu/Nimultilayers [39]; abundant SFs and coherent twins were alsoobserved in 1 nm Ag/Al multilayers [4].

Three mechanisms are likely to be responsible for the for-mation of twins in high SFE metals. First, similar to SFs,coherent R3{111} and incoherent R3{112} twin boundaries(CTBs and ITBs) nucleated in a low SFE seed layer couldpenetrate into a high SFE layer via coherent interfaces. Addi-tionally, once a vertically propagating TB is formed in a highSFE layer, it can often extend across many layers [65]. Sec-ond, CTBs are replicated laterally from a low SFE seed layerinto a high SFE layer. Once the CTBs terminate at the layerinterface, ITBs would have to nucleate inside the high SFElayer to join the variants, increasing accordingly the totalsystem energy. Therefore, energetically, the propagation ofCTBs across layer interface into a high SFE layer is morefavorable than termination [38,39,64,65]. Third, the con-cept of misfit twin-induced alleviation of coherency stressesis less likely to account for the formation of twins in a highSFE layer [39,65].

Commonly, the driving force available to nucleate twinsduring the growth of NMMs stems mainly from coherentstresses. As partial dislocationsmust form prior to the forma-tion of twins, shear stressesmust exist to trigger the formationof partial dislocations. Take Cu/Ni as an example, atoms aretypically attached to the peripherals of terraces during theprocess of island growth.At the free surface ofCu islands thatgrow epitaxially on Ni substrate, there is no stress. However,residual stresses quickly develop in Cu films when movingaway from the free surface. Thus, to introduce coherencystresses in Cu, interfacial shear stress is necessary alongCu/Ni interfaces close to the free surface. This shear stress,τ , may be estimated by [66]:

τ = εE

1 − v

√Eshf

2Ef π x, (2)

where Es and Ef are the Young’s modulus of the substrateand film, respectively, hf is the film thickness, x is the dis-tance from island edge, ε is the misfit strain, and b is the

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The mechanical behavior of nanoscale metallic multilayers: A survey

Burgers vector. The high shear stress estimated at the edgeof the terrace is sufficient to nucleate Shockley partials inCu, causing subsequently the formation of fine twins duringcontinuous growth [64].

3 Mechanical properties

3.1 Yield strength/hardness

Hardness (or, equivalently, yield strength) has been the mostcommonly studied mechanical property of metallic films inview of the significant progress in nanoindentation. Interestin metallic NMMs emanated initially from the order-of-magnitude increase in hardness (and yield strength) achievedby decreasing the layer thickness h [65]. (The hardness of anNMM is obtained by multiplying its tensile yield strength by2.7 [67]). With rapid development of nanotechnology, recentattention has mainly focused on the range of h < 100 nm.In particular, extensive works have been conducted exper-imentally and theoretically on Cu/Ni [30,38,39,65,68–75]and Cu/Nb [1,5,6,42,43,69,74–78] NMMs.

In general, the strength and hardness of NMMs are influ-enced by layer thickness, interface orientation, interfacialstructure, and fabrication method. The hardness of a NMMfabricated via electrodeposition {001} is different fromthat obtained with electrodeposition {111}, despite similarlayer thickness, interface sharpness, and interface orientation[70,72]. Interface orientation strongly affects the hardnessof a NMM system. For instance, a PVD {111} multilayerwith a strong [111] Cu ‖ [111] Ni orientation relationshipnormal to interfaces [38] exhibits a different hardness fromthat of a PVD {001} multilayer having a strong cube-on-cube or [001] Cu ‖ [001] Ni orientation relationship [72].Further, the dependence of NMM hardness upon h remainsa hot topic. Figure 8 presents existing hardness (H) datafor various NMM systems [79]. A variation trend similar topolycrystalline metals is observed, namely, the smaller thestronger. Discussion of the length-scale dependent strength-ening mechanism is left to Sect. 4.1.

For the widely investigated Cu/X NMMs, Table 1 com-pares their peak hardness (Hmax), Young’s modulus mis-match (EX /ECu), and hardness enhancement. The hardnessenhancement is derived from the hardness ratio of Hmax tothe rule-of-mixture estimate (Hrom) from monolithic con-stituent films. Previously, the origin of hardness enhancementhas mostly been discussed in terms of dislocation interactionwith interfaces between elastically mismatched materials,and it has been postulated that the Koehler stress plays adominant role in determining the peak strength, especiallyin systems with large elastic modulus mismatches [79,80].In a multilayer system, as the line energy of a dislocation isproportional to shear modulus μ, dislocations are attracted

Fig. 8 Comparison of hardness versus h−1/2 plots for various metallicmultilayer systems. Reprinted from Ref. [79] with permission

to reside in low modulus layers. However, one key pointthat can be clearly observed from Table 1 is that hardnessenhancement does not correlate with the bulk modulus of theconstituent materials. For example, Cu/Au and Cu/W multi-layers have similar hardness enhancement, yet their Young’smodulus mismatch differs by nearly a factor of six. Accord-ingly, increasing E does not necessarily lead to enhanced H .More generally, it is believed that the strength and interfaceproperties of a multilayer derive more from its interfacialstructure, bonding, and defects [74,81].

3.2 Elastic modulus

As far asmechanical strength is concerned, NMMs are one ofthe strongest synthetic materials ever produced. Apart fromsignificant hardness enhancement, it has been well estab-lished that significant elastic anomalies also exist for manyNMM systems. For instance, the modulus values of Cu/W[36] andCu/Nb [77] increasewith decreasing h and aremuchhigher than those of monolithic films. However, for Cu/Co[41] and Cu/Ru [86], their elastic modulus exhibits a weakdependence on h. For Ag/Ni [37], Ag/Cu [35], Ag/Nb [87],Ag/Co [88], Ni/Ru [17], and Ag/W [89], the modulus evendecreases as h is reduced

ForCu/Wmultilayers prepared by evaporation deposition,the interfaces of Cu on W and W on Cu are asymmetri-cal. During the deposition process, Cu atoms with relativelyhigh homologous temperature have greater mobility than Watoms. Thus, when Cu atoms are deposited onto aW surface,a smooth surface tends to form with relatively low surfaceenergy. By contrast, when W atoms are deposited onto a Cusurface, the vapor atoms are incorporated epitaxially closeto their arrival point owing to their low mobility, and it isdifficult for them to form a smooth surface or diffuse into the

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Table 1 Comparison of peak hardness,Young’smodulusmismatch (EX /ECu) and hardness enhancement Hmax/Hrom for a variety ofCu/Xmultilayersystems

Systems(Cu/X)

Layer thickness,h (nm)

Peak hardness,Hmax (GPa)

Elasticity mismatchEX/ECu

Hmax/Hrom References

Cu/Ni 1.75 6.83 1.65 1.89 [38]

Cu/Au 25 2.45 0.56 1.23 [82]

Cu/Co 1 6 1.75 1.60 [40]

Cu/Fe 5 4.8 1.61 1.49 [83]

Cu/V 2.5 5.2 0.97 1.56 [79]

Cu/Cr 10 6.8 2.40 1.36 [1]

Cu/W 4 8.9 3.30 1.25 [36]

Cu/Ta 30 7.0 1.44 1.08 [84]

Cu/Zr 5 5.8 0.68 1.54 [85]

Cu/Ru 5 8.1 3.58 1.16 [86]

under layer [36]. The intermixing leads to the compression ofout-of-plane interplanar spacing of theW layer, causingmod-ulus enhancement as h is reduced. For the same reason, theenhanced modulus of fcc/fcc Cu/Nb [77] is attributed to thecompressed out-of-plane interplanar spacing of fcc Nb layer.

However, although supermodulus effect (multilayer mod-ulus much higher than those of monolithic films) exists inmost multilayer systems, a drastic softening of 30 %–50 %in elastic modulus is often observed as the periodicity in amultilayer is reduced [35,37,89–91]. For example, forCu/Nb[77], Cu atoms are probably able to penetrate into the loca-tions of incomplete coalescence to form intermixing regionswith amorphous microstructure between grain boundaries inNb layers or at interface when h is further reduced. Fur-ther, investigation of Ag/Nb indicates that free volume in theamorphous alloy region has a negative contribution to themodulus, causing a decrease of modulus with decreasing hbecause more interfaces are present in the multilayer [87].The same phenomenon is found in Cu/Cr, namely, its inden-tationmodulus E exhibits a non-monotonic evolutionwith h,attaining a maximum at h = 25 nm [91]. This unusual varia-tion in E is related to the competition between enhancementeffect induced by compressed out-of-plane interplanar spac-ing of constituent layers and reduction effect associated withthe formation of interfacial amorphous intermixing layers.

Another explanation proposes that the decrease of E withdecreasing h is attributed to the presence of compliant inter-faces [37,88]. Themodulus of amultilayermay be calculatedusing the following equation [81]:

1

E= 2h

(2hiEint

+ 2h − 2hiE0

)−1

, (3)

where hi is the interface thickness, Eint is the interfacemodu-lus, and E0 is the rule of mixture value. Consequently, as theperiodicity is reduced, more compliant interfaces are formedin themultilayer, causing its elastic modulus to decrease with

decreasing h. This result also indicates that there may existinterface layers whose structure is different from the intra-grain crystalline structure, and these interface layers mayaffect the plastic deformation mechanism of NMMs.

3.3 Ductility

Ductility data for NMM films are at present limited sincenanoindentation has been the primary mechanical testmethod. Most of the available engineering strain data areobtained from tensile [78,92] and micropillar compression[5,93] tests. Usually, tensile tests generate much smallervalues, reflecting that tensile failure often involves cracknucleation from edge defects in the thin films. In general,the strength and ductility of a multilayer are mutually exclu-sive, i.e., the ductility of NMMs drops with decreasing h,exhibiting a reverse trend to the strength [5,8,92].

In contrast, compression failure often involves shear local-ization in equiaxed samples machined from a NMM filmand loaded perpendicular to its interfaces [94]. Experimentalresults on the ductility of NMMs obtained by the LosAlamosgroup [5,94] with nanoindentation testing showed that com-pressedCu/NbNMMspillars exhibited a significant ductility.However, the ductility decreased from 36 % to 25 % whenh was reduced from 40 to 5 nm. Further, rolling studies onnanoscale Cu/Nb multilayers [95,96] demonstrated rollingstrains of >60 % with no material failure. However, forCu/Nb multilayers, Misra et al. [97] showed that the rollingstrain to fracture decreased rapidly when h was reduced toless than about 30 nm. Obviously, how to improve the duc-tility of NMMs has become a critical issue for optimizedmaterials selection, design and fabrication.

3.4 Fracture behavior

The selection and design of high-performance NMMs isdriven by optimized combinations of mechanical properties

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The mechanical behavior of nanoscale metallic multilayers: A survey

and requirements for predictable and non-catastrophic failurein service. Therefore, understanding the fracturemechanismsof an NMM system is critical for understanding how it willperform in service. Ultimately, the exploitation of an NMMmultilayer in engineering applications depends on its strengthand fracture toughness. However, so far, the superior strengthof NMMs is achieved at the expense of low ductility andfracture toughness, which limit considerably their practi-cal applications. Similar to the ductility of NMMs, such acontradictory trend may also be attributed to the increasedpropensity of strain localization as the length scale (layerthickness) is decreased.

The fracture behavior of an A/B NMM system consist-ing of alternating ductile (A) and brittle (B) layers may bedescribed using a micromechanics model [8,98,99]. In thismodel, the deformation capability of the ductile A layer isquantitatively evaluated by deriving an equilibrium numberof dislocations that can be accumulated in this layer. Themodel assumes that once a crack is nucleated, a pre-existingmicrocrack will easily propagate to form an opening crackthroughout the whole B layer and reach the A/B interface,with high stress concentration near the crack tips.Crack prop-agation is then a function of applied stress intensity, crack-tipshielding due to plastic deformation, and ability to accommo-date crack-tip dislocation activity without crack advance [8].If the stress intensity near the crack tip is sufficiently large,edge dislocations from the A layer can be generated at thecrack tip, so that the crack can induce plastic shear throughemission of edge dislocations from the crack tip (Fig. 9a).Dislocations thus emitted may have two effects. Firstly, theyblunt the crack tip and reduce stress concentration at the cracktip. Therefore, the fracture progress is suppressed and it ismore difficult to reach the cohesive strength of the A layer.The free-standing layer in front of the opening crack couldthence be easily deformed via dislocation gliding across thewhole layer. Secondly, when these dislocations move to aninterface, a back stress is sent to the crack tip. The backstress will impede further dislocation emission, promoting,therefore, the fracture progress. At a given load level, theequilibrium number of dislocations n is [8,98]:

n = 4π(1 − v)

ln(̃h/̃r

)(K̃app

√h̃

A√2π

sin ϕ cosϕ

2− γ̃

), (4)

where ϕ = 45◦ is the inclination angle of slip plane to theinterface, A ≈ 1, r̄ = 2.7r0/b, r0 is the effective coreradius in A, Kapp = 1.12σapp

√πh is the far field mode I

stress intensity [99], hϕ = h/ sin ϕ, and γ is the surfaceenergy, respectively. For convenience, the following non-dimensional parameters have been introduced:

K̃ = Kapp

μ√b, h̃ = hϕ

b, γ̃ = γ

μb, (5)

Fig. 9 a Sketch of dislocation emitted from interface in Cu/X NMMs.b predicted nmax plotted as a function of h. Reprinted from Ref. [8]with permission

whereμ is the shear modulus. The stress at the blunted cracktip, σ̃tip, is thence related to n and Kapp as,

σ̃rip√n = 2

√2πK̃app

[1 − 3

(sin ϕ cos ϕ

2

)2ln

(̃h/̃r

)]

+ 12A√h ln

(̃h/̃r

) γ̃ sin ϕ cosϕ

2. (6)

When the stress at the crack tip reaches the fracture stressσc of the material (̃σtip = σ̃c), the crack will propagate tothe A layer so that a channel crack is formed. The maximumnumber (nmax) of equilibrium dislocations emitted from thecrack tip prior to cleavage in the A layer can be obtainedfrom Eqs. (4) and (6). In addition, the far-field applied stressintensity under this condition is the fracture toughness of theNMM multilayer, which can be obtained from K̃IC = K̃app.

The predicted nmax for Cu/Nb (see Fig. 9b) exhibits appar-ently a size effect [8], that is, with h increasing from 5 to25 nm, nmax increases sharply. As a larger nmax implies bet-ter plastic deformation capability, theCu layers becomemoreductile, hindering, therefore, crack propagation in the brittleNb layers. The propagation of a microcrack in the Nb layermainly depends on the far field mode I stress intensity (K )

ahead of the microcrack, which scales as h0.5[100]. As aresult, when h is increased, K increases so that both the duc-tility and fracture toughness (KIC) of the NMM decrease.

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Q. Zhou et al.

0.06a bCu. Chen et al.[6]

Cu

Al

Ni

Cu. Wei et al.[4]Cu. Lu et al.[5]Al. Miyamoto et al.[8]Al. Kalkman et al.[7]Ni. Torre et al.[10]Ni. Wang et al.[9]

Ti [13]

Ti [16]

Mg [17]

Co [18]Ti [14]

Mg [19]

Ti present work

Fe. Jia et al.[13]Fe. Wei et al.[14]Ta. Wei et al.[15]Ta. Wei et al.[4]W. Wei et al.[16]V. Wei et al.[17]

α-W, this workW, Wei et al[16]Theoretical estimation

0.05

0.04

0.03m

0.02

0.01

0.00

10 100 1000

Grain size (nm)

10000

0.06

0.05

0.04

0.03

0.02

0.01

0.00100 1000 10000 100000

10000010000100010010

0.6

0.4

0.2

0.0

0.05

0.04

0.03

0.02

0.01100 1000 10000

m

m m

Grain size (nm)

Grain size (nm) Grain size (nm)

c d

Fig. 10 Strain rate sensitivity of a fcc, b bcc and c hcp metals summarized using data from existing literature. d Strain rate sensitivity of bcc W ata grain size smaller than 100 nm. Reprinted from Refs. [102,106] with permission

Meanwhile, a larger K indicates that the microcrack canpropagate more easily to form an opening crack, confirm-ing the prediction [8] that at the critical condition of hcri,a transition in fracture mode (from opening to shear) mayoccur. These results suggest that rather than the strengthen-ing mechanism, the constraint effect imposed by the ductileA layer on the brittle B layer is the dominant factor that con-trols the modulation period and modulation ratio dependentfracture mode in A/B NMM systems [101].

3.5 Strain rate sensitivity

Strain rate sensitivity (m) is a crucial parameter that couldshed light on the rate controlling mechanisms in of NMMsduring plastic deformation. It describes the dependence offlow strength σ on the rate of strain ε̇ as [102]:

m = ∂ ln σ

∂ ln ε̇=

√3kBT

V ∗σ, (7)

where V ∗ is the activation volume. Equation (7) suggeststhat sampling volume is involved in dislocation activities,the latter also responsible for NMM plastic deformation.

The variation trends of strain rate sensitivity in NMMswith h are complex due to the coexistence of two differ-ent constituent phases. Before clarifying the rate-dependentdeformation characteristics ofNMMs, the strain rate sensitiv-ity of single-phase nanoscrystalline (NC) metals needs to beaddressed. Experimentally, it has been found thatm is highlysensitive to the average grain size (d) or nanotwin thickness[103–105]. It has also been found that the size dependence ofrate-sensitive parameters is closely related to the lattice struc-ture of NC metals. Figure 10a [102] shows thatm for severalfccmetals increasesmonotonicallywhen d is decreased,withm > 0.1 for NC fcc metals. In contrast, Fig. 10b [102] showsthat m for bcc metals has the opposite dependence on grainsize, with m < 0.1 for NC bcc metals. However, Fig. 10cindicates that hcp metals have a similar trend as that of NCfcc metals [106].

For multilayer thin films, the fundamental questions aboutstrain rate sensitivity (m) are [107]: (1) competition or coop-eration effect between the two constituent phases (e.g., fccvs. bcc) at nanoscale, given that they have radically differentvariation trends ofmwithgrain sized, as compared inFig. 10;(2) influence of dissimilar interface structure (e.g., coherentvs. incoherent) in NMMs on m; (3) possibility of other char-

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The mechanical behavior of nanoscale metallic multilayers: A survey

acteristic microstructures, such as grain size or twins, thatmay have an effect equal to or greater than that of the inter-face.

First, consider the influence of constituent layers, i.e., fccversus bcc, or fcc versus hcp.With theNMMs taken simply asa composite, their properties are affected by each constituentphase. A rate jump compression was used by Carpenter et al.[71] test to study rate effects in Cu–Ni multilayers. Obtainedroom-temperature values of m varied from 0.013 to 0.020as the compressive stress was increased from 660 to 1800MPa. These m values are similar to those for NC fcc metals.The same trend (m decreasing with increasing h) was alsodetected in Ag/W [23]. Results presented in Fig. 10b showthat the bcc W has an opposite dependence of m on d; how-ever, as the grain size dropped below a critical value (e.g.100 nm for W), elevated m was observed due to GB-relateddeformation mechanisms (Fig. 10d [102]). As the grain sizesin both Ag and W layers have been found to scale positivelywith h [23], the strain rate sensitivity of the Ag/W NMMsshould decrease with increasing h when h falls within thenano regime. This is because enlarged grain size in Ag andW layers will lead to reduced strain rate sensitivity in Ag/Wmultilayers, and the plasticity is shared by both Ag and Wphases. However, it is interesting to notice that the m valuesof Ag/W multilayers with h larger than 50 nm are almostequal to that of Ag film since plasticity is localized in thesoft fcc Ag layer. In comparison, for Cu/Nb multilayer withh = 10 nm [42], m is equal to that of bcc Nb film. The rateof climb in Cu layers will be much larger than that in the Nblayers. Thus, the resistive force induced by increasing strainis easier to be released by the process of dislocation annihila-tion, assisted by climb in Cu layers. As a result, the majorityof the extra load required to overcome strain hardening in aCu/Nb multilayer is taken up by Nb layers. The multilayerexhibits, therefore, similar rate-controlling characteristic ofthe Nb film.

Second, to clarify further the creepmechanisms during theindentation process in NMMs, Zhu et al. [38,41,108] carriedout a series of room temperature indentation creep testing tomeasure the strain rate sensitivity and creep stress exponentn∗. As for indentation creep with a self-similar indenter, n∗may be extracted through the following relation [109]:

−n∗ ln H(t) = ln B − Q

RT+ ln t, (8)

where H(t) is the instantaneous hardness, t is the time forload holding, B is a dimensional scale constant and Q isthe activation energy. In general, the stress exponent n∗should scale inversely with m. For Cu/Ni [38] and Cu/Co[41] with coherent interfaces, the stress exponent n∗ wasfound to increase with decreasing h. As the coherent super-lattice structure forms when h is reduced, the density of edge

dislocations settled at the interfaces declines, thus reducingthe effective diffusion paths provided by the interfaces. Con-sequently, the stress exponent increases and the strain ratesensitivity decreaseswith decreasing h. In contrast, forAg/Fewith incoherent interfaces [108], as h is reduced, a monotonedrop in stress exponent and increase in strain rate sensitiv-ity is observed. As a creep process is typically dominatedby the mechanism of dislocation glide-climb, the increasedfraction of grain boundaries and incoherent interfaces pro-vides effective diffusion paths for creep climb because grainboundaries and incoherent interfaces can be the source toemit and absorb dislocations [110]. As a result, it is not sur-prising that the creep process exhibits a higher strain ratesensitivity when h is reduced.

Third, grain size as well as twin spacing play importantroles in controlling the strain rate sensitivity of NMMs. Con-sider, for instance, the influence of grain size in both A and Bconstituent layers on the strain rate sensitivity of A/B multi-layers. Given the contribution from GB, the effective rule ofmixtures (ROM) for evaluating the strain rate sensitivity oftwo phase (A and B)materials may bemodified. On the otherhand, the dragging force that the interfaces exert on a singleslip dislocation increases rapidly with decreasing periodic-ity, as layer thickness and grain size are both reduced. Theviscous glide velocity then falls below the dislocation climbvelocity, so that viscous glide will dictate the rate-controllingprocess and the value ofm. In Ag/Cumultilayers, a transitionof creep deformationmechanism fromdislocationmovementto grain boundary sliding occurs as h is less than 15 nm [35].In Ag/Ni multilayers, the dependence of creep rate on layerthickness reveals that grain boundary deformation is moredominant for h < 4 nm [111]. In this case, when the layerthickness is small enough, the strain rate sensitivity and creeprate of the multilayer should always increase with decreas-ing h, independent of interface structure [38,41]. Apart fromgrain size, the decreasing rate sensitivity found in Cu/Zr andCu/Cr [107] is potentially a result of decreasing twin fractionin Cu at small h. In addition, the non-monotonic evolutionof m with h observed in Cu/X multilayers may be explainedby a competition between monotonically increased interfacedensity and decreased twin boundary density [112].

4 Plastic deformation

4.1 Length-scale-dependent deformation mechanisms

NMMmaterials are rather suitable for fundamental studies oflength scale effects, in themicrometer to nanometer thicknessrange, on deformation mechanisms of metallic nanocom-posites. Built upon previous experimental and theoreticalstudies, Misra et al. [76] produced Fig. 11 to summarizedeformation regimes in metallic multilayer thin films hav-

123

Q. Zhou et al.

interface crossing

B

A

B

A

B

A

h

dislocation

dislocationbowing

Str

engt

h

h

h

pile-up

deformation assistedby mechanical advantageof dislocation pile-ups

deformation involves glideof single dislocationsconfined to individual layers

sub-micronsto microns

Layer thickness

few nmto a fewtens of nm

∼ 1–2 nm

σ ∝ h -1/2

σ ∝

σ ≠ f(h)

h

In(h/b)

Fig. 11 Deformation mechanisms active at different length scales. Reprinted from Ref. [76] with permission

ing varying individual layer thickness h. Under a constantmodulation ratio of 1, the hardness/strength curve of NMMsusually exhibits three distinct regions:Hall–Petch (H–P), sin-gle dislocation, and interface crossing.

4.1.1 Hall–Petch regime

At sub-micrometer to micron length scales, the applicabil-ity of the classical H–P strengthening relation is built uponthe premise that dislocations piling up against an interfaceare responsible for the yielding behavior of lamellar metals[73,113]. The success of the H–P relation in describing thestrength of many polycrystalline materials suggests that itsorigin is very fundamental, and that similar behavior shouldbe observed inmultilayers (including NMMs). Thus, accord-ing to the H–P relation, the yield stress σys of a NMMmultilayer is related to its layer thickness h as [76]:

σys = σ0 + kh−1/2. (9)

Figure 7 demonstrates that a linear fit to the hardness ofNMMs at coarse length scales is consistent with the H–Ptheory. In this theory, the interface boundary is assumed toact as an obstacle to dislocationmotion. Dislocations emittedfrom a source move along the same slip plane and propagatetowards the interface. Once the lead dislocation is stoppedby the interface, the trailing dislocations stop behind it dueto mutual repulsion, causing dislocation pileup at the inter-face. The number N of dislocations in a pileup subjected toan applied shear stress τ scales with the distance L betweenthe source and obstacle, as [9]:

N = π L(1 − v)(τ − τ0)

μb, (10)

where v and τ0 are the Poisson ratio and lattice friction stress,respectively. When the stress concentration at the pileupeventually exceeds the interface barrier, the NMMplasticallyyields. Since the H–P slope represents the strength (τint) ofthe interface barrier, the peak strength of the NMM may beestimated from the measured slope by [76]:

τint = k2 π(1 − v)

μb. (11)

By multiplying τint with the Taylor factor, theoretical esti-mates of the ultimate peak strength may be obtained forNMMs.

4.1.2 Single-dislocation regime

When the layer thickness h is further reduced, the H–P effecton strength levels off in the vicinity ofh ∼ 50nmeven thoughthe strength continues to increasewith decreasingh [79]. Thisbreakdownoccurs, in part, becauseEq. (10) treats the numberof dislocations N as a continuum, valid only when N � 1.In fact, for d ∼ μ m or larger, dislocation sources withingrain interiors are ubiquitous and operate at low stresses.When h approaches several nm, slip occurs by motion ofsingle dislocations (as opposite to continuum-scale pileups)and the interfaces become the controlling parameter in plas-tic deformation [114]. Under such conditions, dislocationsources shift to the interfaces and the stress to operate them,which depends on the h-dependent interfacial structure. The

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The mechanical behavior of nanoscale metallic multilayers: A survey

Fig. 12 Schematic of confined layer slip mechanism in multilayerstructures. Dislocation loops glide individually in each layer and depositdislocations in the interface plane. Reprinted from Ref. [116] with per-mission

strengthening mechanism has been described [76,115,116]as an effect of confined layer slip (CLS) of single-dislocationloops within the confined geometry of NMM, as shown inFig. 12 [116]. Experimentally, these loops are shown to orig-inate from existing threading dislocations, from interfaces,and from interactions with other dislocations [56,115–118].

Based on the CLS model [76], plastic yielding wouldoccur when dislocations are curved into a semicircle withinthe confined geometry of a constituent layer. Concerningdislocation core spreading, residual interface stress, andinteraction between gliding dislocations with stress fieldsarising from misfit dislocation arrays deposited at the inter-face, the refined CLS is generally believed to be an excellentdescriptor for strength, given as [76]:

σCLS= Mμb

8π hϕ

(4 − v

1 − v

)ln

(αhϕ

b

)− f

h+ μb

s(1 − v), (12)

where hϕ = h/ sin ϕ is the layer thickness measured par-allel to the glide plane. ϕ is the angle between the slipplane and the interface. α is the core cut-off parameter.f is the characteristic interface stress of the multilayer.s = 2bm0/ε0 is the mean spacing between misfit disloca-tions deposited at the interface,m0 being the strain resolutionfactor. And ε0 is the in-plane plastic strain [76]. Atten-tion should be paid to the interface stress ( f ) that arisesfrom elastic deformation of the interfacial region. Undertensile loading parallel to the interface, the applied stressmust also do work against interface stress, which is usu-ally negative for metal systems. However, for indentationhardness testing, the interface stress would assist the appliedstress [76].

Equation (12) provides a good fit to existing strength dataof most NMM systems as h is reduced from tens of nanome-ters to several nanometers. However, at very small h (lessthan core cut-off dimension), the equation used to calculatethe dislocation self-energy is no longer valid because thelog term in the equation becomes negative, leading to neg-ative values of the CLS stress. Note that the model predictsincreasing strength with decreasing h, while experimentaldata indicate that a peak strength is achieved at h ∼ 1–2 nmand, as h is reduced below 1 nm, a drop in strengthmay occuras well. Consequently, the CLSmodel is not applicable whenh is less than about 2 nm.

4.1.3 Interface-crossing regime

Figure 8 indicates that when h is sufficiently small, itseffect on strength levels off, until a decrease in strengthis observed, which is popularly called the inverse H–Peffect, as observed in bulk nanocrystalline metals. Withinthis regime, the mechanism of interface crossing or dislo-cation transmission controls the strength. The saturation orplateau in strength has been attributed to the stress exceedingthe threshold needed for interfacial transmission [76,119].In the interface-crossing regime, it has been found that thestrength is predominantly related to interface structure barri-ers between two constituent layers. Both coherent and inco-herent interfaces can cause significant strength enhancementfor amultilayer system relative to its bulk counterparts. How-ever, experiments show that the strengthening mechanismsfor systems having coherent interfaces are different fromthose with incoherent interfaces [120–122]. In the followingsections, the mechanical properties of multilayer thin filmsarising from different structures of interfaces and their inter-action with mobile dislocations are discussed in sequence.

For coherent interfaces such as epitaxial Cu/Ni, geomet-rical barriers to transmission are absent, in the sense that adislocation can glide across an interface with ease, leavingsimply a step at the interface. Despite this, the strength ofa multilayer thin film with coherent interfaces is larger thanthose of its bulk materials. Potential mechanisms proposedto interpret this anomalous interface effect include imagestress strengthening [79,80,123], coherent stress strengthen-ing [74,124,125], misfit dislocations strengthening [74,76,126], chemical mismatch strengthening [4,40,74], and solidsolution strengthening [127].More precisely, withmechanis-tic underpinnings of the interface-dependent strengtheningmechanism, the interface strength barrier resistance τint maybe expressed as [40]:

τint = τK + τKe + τcoh + τd + τch, (13)

where τK is Koehler stress originating from modulus mis-match, τKe is the modification to Koehler stress due to

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Q. Zhou et al.

variation of elastic modulus in each layer [74], τcoh is derivedfrom coherency stress, τd is determined bymisfit dislocationsdue to lattice mismatch, and τch is the chemical interac-tion term related to stacking fault energy difference betweenconstituent layers. The relative contribution of each termappearing in Eq. (13) has been studied for Cu/Ni and, toa lesser extent, Cu/Co, as discussed below.

Previously, modulus mismatch has been considered as asignificant barrier to dislocation transmission. In an A/B sys-tem, since the energy/length of a dislocation is proportionalto shear modulus μ, dislocations are attracted to reside inthe lower modulus layer. As the influence of attractive orrepulsive image force τK on dislocation is dependent on thedifference in dislocation line energy between A and B layers,it is proportional to the modulus mismatch as [4,80]:

τK = μA(μB − μA)b sin θ

4π(μB + μA)h, (14)

where θ is the smallest angle between the interface and glideplanes. It becomes obvious from Eq. (14) that the magnitudeof τK exhibits a significant dependence on h,being 0.002GPawhen h = 100 nm, but rising rapidly to 0.18 GPa whenh = 1 nm for Cu/Ni. In addition, as predicted in Sect. 3.2,the elasticmodulus is not a constant as h is varied and, further,τKe is the modification to the Koehler stress. Atomistic sim-ulations predict that the barrier due to modulus mismatch inCu/Ni multilayers is 0.01μ, nearly independent of interfaceorientation and dislocation character [74]. When the layerthickness is reduced to a value comparable to dislocation corewidth, the Koehler stress may decrease considerably [74].

Lattice mismatch δ = a0/a0 is another key parameter,which represents the level of elastic strain with respect tothe stress-free reference state. The coherency stress is deter-mined by lattice mismatch, though coherency is only likelyfor multilayers having small lattice mismatch. According tothe coherent strain theory, the alternating compressive andtensile in-plane stress fields predicted by Eq. (2), which caninhibit dislocation motion, could lead to enhanced strengthand hardness of multilayers. When a slip commences, it maybe confined by oppositely signed compressive and tensile in-plane stresses in the adjoining layers. Macro-yielding is thenexpected when the applied stress is sufficient to eliminate thealternating signed stresses [74].

For multilayer systems having large lattice mismatch, themisfit is too large to achieve coherency in these systems,and hence misfit dislocations will be introduced to accom-modate a portion of the misfit between the two constituentlayers when h is larger than the critical layer thickness hc forcoherency loss. As a result, the interface barrier for multilay-ers with larger lattice mismatch is attributed to the spacing ofmisfit dislocations at the interface. Using atomic simulations,Hoagland et al. [75] examined slip behaviors in coherent

and semi-coherent metallic bi-layered composites and con-cluded that semi-coherent interfaces could act as barriers toslip because of interaction between misfit and glide dislo-cations. Mathematically, the important role played by misfitdislocations in interface strengthening may be described as[128]:

τd = αμ

(δ − b

2h

), (15)

where α is Saada’s constant.Chemical mismatch also contributes, though less signifi-

cantly, to interface strength. As dislocation line energy tendsto increase with SFE γ [129], a mismatch in γ can generate aforce as the dislocation moves across an interface. In an A/Bmultilayer system, the chemical mismatch, τch, arising fromthe SFE difference between A and B, may be approximatedas [4,40]:

τch = γB − γA

b. (16)

Incoherent interfaces are often present in non-isostructuralfcc/bcc systems. Barriers to transmission of interfaces withweak bonding are typically caused by dislocation core delo-calization and dislocation trapping in a low energy state (seeSect. 2.4). Transmission of such an interface requires com-paction of dislocation core to nucleate amobile dislocation inthe adjacent crystal [77]. It is often believed that the strengthdisplayed by an fcc/bcc interface tends to exceed that of anfcc/fcc interface, though opaque systems tend not to havelarge coherency stresses [130]. Incoherent interface barriersare often attributed to the low shear strength of interfaces andthe resultant trapping of mobile dislocations [54]. Interfacialsliding generates an attractive force on mobile dislocationsand allows for core spreading in the interface [53], thushindering dislocation transmission. However, atomistic sim-ulation results show that dislocation glide and climb at aninterface may aid slip transmission [110,131]. In addition,while interfacial line defects (dislocations and disconnec-tions) formed at an interface will interact with mobile dislo-cations to hinder successive interface slip on the sameor adja-cent slip systems in fcc/fcc NMMs, these will hardly workin fcc/bcc NMMs due to compaction of dislocation core.

4.2 Plastic instability

Deformation instability is a bifurcation of strains away fromthe uniform state. Localization of plastic strains is a commondeformation-induced instability inNMMs.How it happens isrelated to both the microstructure and the way in which plas-ticity ismediated prior to localization.Generally, the ductilityof NMMs is limited by the eventual formation of localizedbands of intense plastic strain.

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The mechanical behavior of nanoscale metallic multilayers: A survey

Fig. 13 Schematic illustration of two different deformation mechanisms corresponding to buckling-assisted layer rotation of a h = 25 nmmultilayer and dislocation plasticity-dominated shearing of b h = 250 nm Au/Cu multilayer. Reprinted from Ref. [135] with permission

Shear banding has been extensively studied to reveal themechanisms underlying inhomogeneous plastic deformationin nanocrystalline, amorphous solids and nanomultilayers.For NMMs, the formation of shear bands is attributed todiminished strain hardening ability and low strain rate sen-sitivity when the number of dislocations is limited and themobility of interfaces increased. The hindered dislocationmotion inside small grains is expected to make the interfacesmore active to accommodate plastic deformation, resulting ininterface-related deformation behaviors, such as grain rota-tion and grain boundary sliding. Works by Zhang et al. [132]and Wen et al. [35] revealed an increasing tendency of shearbanding in nanometer-scale Cu/Au and Cu/Ag multilayersunder indentation and attributed this phenomenon to thelikely occurrence of grain boundary sliding.

Based on discussion presented in the previous sections,one can see clearly that individual layer thickness h is a keyparameter to decide the mechanical properties of NMMs.Deformation instability (shear banding) is no exception.Experimental results of Au/Cu NMMs [132] demonstratethat when h falls within the nanometer regime, inhomoge-neous shear banding becomes prevalent. Additionally, as his reduced, the width of shear bands decreases while themaximum interface kink angle and pileup height increase[132–134]. Along with further microscopic observations,two different types of interface morphology have been iden-tified as h is varied [5,6,135]: one is caused by layer rotation(Fig. 13a [135]), and the other arises from dislocations cut-ting across the interfaces (Fig. 13b [135]). The rotation andlocalization of strain within the shear band implies two com-peting layer-geometry-based mechanisms. At the nanometerscale, buckling-assisted GB sliding causes plastic instabilityof NMMs, while at the sub-micron (or larger) scale, disloca-tion plasticity dominates plastic instability [82].

For NMMs, another sound explanation of the length-scale-dependent shear banding behavior is the differentmechanisms that control the deformation process [42,136].

When deformation is controlled by slip of single dislocationsin confined layers, both constituent layers of a NMM candeform homogeneously and hence no shear band is formed.When h falls within the regime where there occur singledislocations cutting across interfaces, dislocation lines arenot parallel across the hetero-interfaces, especially in fcc/bccNMMs. As a result, crossing of single dislocations is difficultexcept in a particular slip system. When an indentor tip pen-etrates the multilayer system, the stress concentration thusinduced can rotate the layers and, once an adequate amountof rotation has taken place, the particular slip system can beturned into an easy shear direction. As a result, shear insta-bility may suddenly occur when the applied stress is greaterthan the critical value required for dislocation transmissionin this direction [42].

5 Summary

The proliferation of publications on NMM thin films as aspecial class of structural composite materials is an indica-tion of intense interest on this subject worldwide. In thissurvey, we have attempted to focus on the broad variationtrends exhibited by the mechanical properties of NMMs,which may be rationalized using physically sound interface-related deformation mechanisms. Length scale and interfacestructure are widely considered two key factors dictating themechanical performance of NMMs. Additionally, synthesisapproach, testing method, grain size and morphology, andspecial microstructure such as twins and bubbles also playimportant roles in the unique strengthening and plastic defor-mation behavior of NMMs.

After all, the mechanical properties of NMMs are closelyrelated to their microstructure, in particular, the interfacestructure. Understanding the interface and its deformationbehavior holds the key to future development of high per-formance NMM systems, and controlling the microstructure

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Q. Zhou et al.

of NMMs can aid the design and manufacture of reliablemultilayer systems and nanostructured composites. Abun-dant research opportunities exist in this area: in additionto the unresolved issues outlined in the present survey, themechanics of creep, fatigue, fracture, and irradiation formultilayer systems is still in the early stage of data accu-mulation. An in-depth understanding of these issues willcontinue to be vigorously sought and, given the rapid devel-opment of relevant nanotechnology, appears to be in goodsight.

Acknowledgments This work was supported by the National Nat-ural Science Foundation of China (Grants 51171141, 51271141, and51471131) and the Program for New Century Excellent Talents in Uni-versity (Grant NCET-11-0431).

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